Abstract: New parameters can be introduced to expand families of distributions for added flexibility or to construct covariate models. Introduction of scale parameter usually leads to the accelerated life model, and taking powers of the survival function introduces a parameter that leads to the proportional hazard model of Morgenstern gumbel bivariate distribution was applied to find the diurnal rhythm of leptin depends on energy, or carbohydrate, availability, not intake, and exercise has no suppressive effect on the diurnal rhythm of leptin beyond the impact of its energy cost on energy availability.